Effects of surface roughness on generalised Rayleigh waves in elastic waveguides

This work examines the propagation of Rayleigh surface waves in an elastic half-space covered by a layer with spatially varying surface corrugation. The mathematical model is established within the framework of two-dimensional linear elasticity, considering general roughness profiles for both the upper free surface and the interface of the layer. A perturbation method is employed to derive analytical expressions for the displacement fields, and dispersion relations are obtained by enforcing the relevant boundary and continuity conditions. The influence of surface corrugation parameters on phase velocity and wave propagation is examined numerically for periodic roughness profiles using selected real material models. The results demonstrate that both the amplitude and geometric characteristics of the surface irregularities have a pronounced impact on the dispersion behaviour of Rayleigh waves. These findings provide new insights into wave propagation in layered elastic media with irregular boundaries and may inform future applications in wave-based sensing, nondestructive evaluation, and acoustic material design.